It's been working fine for several days but on reading this I'm now worried I'm going to fry something unless I use a transistor. What would happen if the LCD drew too much current?
I just put my multimeter in series with the power to the LCD backlight and it's reading 8ma at full brightness, 4ma at half. So I guess if 20ma is the upper limit I'll be totally fine without adding a transistor. I have a 330ohm resistor protecting the backlight - sounds like I could drop that value a little and get a bit more brightness?